but both are incorrect (though there is a sense in which 'II' may contain a grain or two of truth in it).

Things DO indeed change and sometimes these changes happen right before our eyes. Often, we simply don't realize that real change has occurred.

For instance, once upon a time the educational norm in society was the:

'All-PUSH Philosophy of Learning':==========="Children must be PUSHED to learn math (or anything else for that matter)" (A1)

This was a near-universal belief about the 'right way' to 'teach children', commonly held I believe around the same time when, in polite society, it was quite strongly believed that:

- -- "Children should be seen and not heard" (B); and

- -- "Spare the rod, spoil the child" (C).

Of course, even in those dark times there were always people who didn't abide by society's diktats such as the above, but rather attempted to use their common sense to guide them how children should be treated - these, however, were the societal norms.

Things have changed somewhat since then. Nowadays, the beating of children even by their own parents is generally frowned upon by society - and those parents who beat their children may even face the wrath of the law, not to mention its long arm.

Children are nowadays expected to be seen AND heard in society - and generally, it is found, they do pretty well in their social interactions (except for some extremely boisterous children, whose uncouth behavior may actually be derived from some conflicts their parents may have with the new changing societal norms).

Towards the end of the 19th Century, Maria Montessori (amongst other thought leaders) had pioneered a rather different philosophy of education, which depended entirely on the child's inherent 'propensity to learn' and slowly things have been changing in society at large.

Nowadays, the rule has become:

The 'PUSH + ENCOURAGEMENT Philosophy of Education':==========="Children need to be PUSHED to learn - but it may be useful also to ENCOURAGE them to learn" (A2).

According to Robert Hansen (RH) dt. Aug 20, 2013 5:43 PM, http://mathforum.org/kb/message.jspa?messageID=9227118:>> "My theory of education as it relates to the behavioral > elements is that it requires both pushing and > encouragement. How much of each depends on the student > and their current state. Ultimately, you are modeling > their own self discipline, which takes quite a bit of > time on average". >(I haven't been able to figure out quite what RH means by: > "Ultimately, you are modeling their own self > discipline, which takes quite a bit of time on average.>Obviously, I shall have to find out).

Towards a modern philosophy of education:===========By no means is the following the norm as yet. But I personally believe that the societal trend is towards the following philosophy of education:

"Children should be ENCOURAGED to learn (math; everything else). If the ENCOURAGEMENT is effective, then the specific child is likely to learn how to PUSH him-/herself to overcome all the difficulties and barriers that he/she will inevitably encounter while working to pick up the needed knowledge" (A3).

It is my belief that this approach would lead to the most effective possible means for children to learn (math; all other disciplines as well).

I want to get this off while my Internet connection is up and running, so I'm not explicating how much truth there may be in 'II' above.